Search found 30 matches
- Fri Nov 25, 2011 10:38 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Maximum & Minimum Values
- Replies: 3
- Views: 2776
Re: Maximum & Minimum Values
For proving MINIMUM VALUE \[x + y + z = 6 \] \[=> (x + y + z)^2 = 36 \]\[=> x^2 + y^2 + z^2 + 2(xy + xz +yz)= 36\] \[\frac{1}{2}(x^2 + y^2) + \frac{1}{2}(x^2 + z^2)+ \frac{1}{2}(y^2 + z^2) + 2 (xy + yz + xz) = 36\] \[x^2 + y^2 \geq 2xy \] \[=> 3(xy + yz + xz)\leq 36\] \[=> 2(xy + yz + xz)\leq 24\] \...
- Fri Nov 25, 2011 10:20 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Chess Game!
- Replies: 6
- Views: 3999
Re: Chess Game!
There's no need to be sorry.
- Thu Nov 24, 2011 4:58 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Maximum & Minimum Values
- Replies: 3
- Views: 2776
Re: Maximum & Minimum Values
Got the solution.
- Wed Nov 23, 2011 11:38 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Maximum & Minimum Values
- Replies: 3
- Views: 2776
Maximum & Minimum Values
Let x, y and z be real numbers such that x + y + z = 6. Prove that at least one of the numbers (xy + yz), (yz + zx) and (zx + xy) is not greater than 8 and all of them are at most 9.
- Tue Nov 22, 2011 9:25 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Chess Game!
- Replies: 6
- Views: 3999
Re: Chess Game!
You've written: \[\frac{x!}{2!(x - 2)!}= \frac{x^2 - 1}{2}\]
Shouldn't it instead be as follows?
\[\frac{x!}{2!(x - 2)!}= \frac{x^2 - x}{2}\]
Shouldn't it instead be as follows?
\[\frac{x!}{2!(x - 2)!}= \frac{x^2 - x}{2}\]
- Tue Nov 15, 2011 5:49 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Chess Game!
- Replies: 6
- Views: 3999
Re: Chess Game!
Your answer being?
- Tue Nov 15, 2011 12:56 am
- Forum: National Math Olympiad (BdMO)
- Topic: Chess Game!
- Replies: 6
- Views: 3999
Chess Game!
AoA!
A group of 61 students is divided into 3 subgroups. Two students play a game of chess (only once) if and only if they are in the same subgroup. Find a partition such that the total number of games is a multiple of 61.
What do you say?
A group of 61 students is divided into 3 subgroups. Two students play a game of chess (only once) if and only if they are in the same subgroup. Find a partition such that the total number of games is a multiple of 61.
What do you say?
- Fri Nov 04, 2011 9:06 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Polynomial function
- Replies: 1
- Views: 2245
Polynomial function
Can you find a polynomial f ∈ Z[X] such that f(Z) ⊂ N and f takes the value −2005?
Need answer quickly!
Need answer quickly!
- Fri Nov 04, 2011 12:29 am
- Forum: National Math Olympiad (BdMO)
- Topic: Integers
- Replies: 5
- Views: 3474
Re: Integers
Another question on integers:
- Prove that the product of four consecutive positive integers is never a perfect square.
- Prove that the product of four consecutive positive integers is never a perfect square.
- Fri Nov 04, 2011 12:12 am
- Forum: National Math Olympiad (BdMO)
- Topic: Algebra: Inequalities
- Replies: 14
- Views: 8080
Re: Algebra: Inequalities
I understood rearrangement inequality. However, I'm not familiar with this notation/method (quote below). Could anyone kindly explain?
Nadim Ul Abrar wrote:a) rearrangement .
b)
$a^{4}+b^{4}+c^{4}=3[4,0,0]$
$abc(a+b+c)=3[2,1,1]$
$[4,0,0] \geq 3[2,1,1]$
so proved